Part IV Significantly Different: Using Inferential Statistics Chapter 16  Predicting Who’ll Win the Super Bowl: Using Linear Regression

What you will learn in Chapter 16 How prediction works and how it can be used in the social and behavioral sciences How and why linear regression works predicting one variable from another How to judge the accuracy of predictions The usefulness of multiple regression

What is Prediction All About? Correlations can be used as a basis for the prediction of the value of one variable from the value of another Correlation can be determined by using a set of previously collected data (such as data on variables X and Y) calculate how correlated these variables are with one another use that correlation and the knowledge of X to predict Y with a new set of data

Remember… The greater the strength of the relationship between two variables (the higher the absolute value of the correlation coefficient) the more accurate the predictive relationship Why??? The more two variables share in common (shared variance) the more you know about one variable from the other. 

The Logic of Prediction Prediction is an activity that computes future outcomes from present ones What if you wanted to predict college GPA based on high school GPA?

Scatter Plot

Regression Line Regression line – reflects our best guess as to what score on the Y variable would be predicted by the X variable. Also known as the “line of best fit.”

Prediction of Y given X = 3.0

Error in Prediction Prediction is rarely perfect…

Drawing the World’s Best Line Linear Regression Formula Y=bX + a Y = dependent variable the predicted score or criterion X = independent variable the score being used as the predictor b = the slope direction and “steepness” of the line a = the intercept point at which the line crosses the y-axis

Slope & Intercept Slope – calculating b Intercept – calculating a

How Good Is Our Prediction? Standard error of estimate the measure of how much each data point (on average) differs from the predicted data point or a standard deviation of all the error scores The higher the correlation between two variables (and the better the prediction), the lower the error will be

Using the Computer SPSS and Linear Regression

SPSS Output What does it all mean?

SPSS Scatterplot

The More Predictors the Better? Multiple Regression Multiple Regression Formula Y = bX1 + bX2 + a Y = the value of the predicted score X1 = the value of the first independent variable X2 = the value of the second independent variable b = the regression weight for each variable

The BIG Rule… When using multiple predictors keep in mind... Your independent variables (X1,, X2 ,, X3 , etc.) should be related to the dependent variable (Y)…they should have something in common However…the independent variables should not be related to each other…they should be “uncorrelated” so that they provide a “unique” contribution to the variance in the outcome of interest.

Glossary Terms to Know Regression line Error in prediction Criterion Line of best fit Error in prediction Standard error of the estimate Criterion Independent variable Predictor Dependent variable Y prime Multiple Regression